Painlevé analysis,conservation laws,and symmetry of perturbed nonlinear equations

We consider the Lie-Backlund symmetries and conservation laws of a perturbed KdV equation and NLS equation. The arbitrary coefficients of the perturbing terms can be related to the condition of existence of nontrivial LB symmetry generator. When the perturbed KdV equation is subjected to Painlevé analysisa la Weiss, it is found that the resonance position changes compared to the unperturbed one. We prove the compatibility of the overdetermined set of equations obtained at the different stages of recursion relations, at least for one branch. All other branches are also indicated and difficulties associated them are discussed considering the perturbation parameter to be small. We determine the Lax pair for the aforesaid branch through the use of Schwarzian derivative. For the perturbed NLS equation we determine the conservation laws following the approach of Chen and Liu. From the recurrence of these conservation laws a Lax pair is constructed. But the Painlevé analysis does not produce a positive answer for the perturbed NLS equation. So here we have two contrasting examples of perturbed nonlinear equations: one passes the Painlevé test and its Lax pair can be found from the analysis itself, but the other equation does not meet the criterion of the Painlevé test, though its Lax pair is found in another way.     

First example of the C-alkylation of indoles with Baylis-Hillman acetates

Baylis-Hillman acetates undergo S_N2′ allylic substitution with indoles in the presence of 20 mol % of indium tribromide under mild conditions to afford a new class of substituted indoles in high yields with (E)-stereoselectivity. The stereochemistry of the products was assigned by various NMR experiments.     

Spray reagents for the detection of amino-acids on thin-layer plates

Three spray reagents for the detection of amino-acids on silica-gel thin-layer chromatography plates are reported. The reagents produce various colours, which may be used to identify some of the amino-acids directly, and assist in their detection.     

Ultrafast energy-electron transfer cascade in a multichromophoric light-harvesting molecular square

A molecular square with dimensions of about 4 nm, incorporating sixteen pyrene chromophores attached to four ditopic bay-functionalized perylene bisimide chromophores, has been synthesized by coordination to four Pt(II) phosphine corner units and fully characterized via NMR spectroscopy and ESI-FTICR mass spectrometry. Steady-state and time-resolved emission as well as femtosecond transient absorption studies reveal the presence of a highly efficient (>90%) and fast photoinduced energy transfer (k(en) approximately equal to 5.0 x 10(9) s(-1)) from the pyrene to the perylene bisimide chromophores and a very fast and efficient electron transfer (>94%, k(et) approximately equal to 5 x 10(11) up to 43 x 10(11) s(-1)). Spectrotemporal parametrization indicates upper excited-state electron-transfer processes, various energy and electron-transfer pathways, and chromophoric heterogeneity. Temperature-dependent time-resolved emission spectroscopy has shown that the acceptor emission lifetime increases with decreasing temperature from which an electron-transfer barrier is obtained. The extremely fast electron-transfer processes (substantially faster and more efficient than in the free ligand) that are normally only observed in solid materials, together with the closely packed structure of 20 chromophoric units, indicate that we can consider the molecular square as a monodisperse nanoaggregate: a molecularly defined ensemble of chromophores that partly behaves like a solid material.     

A radiochemical study of the kinetics of exchange between manganese oxides and some cations in solution

The kinetics of the exchange between⁵⁶Mn-labelled manganese dioxide and cations in aqueous solution was studied by measuring the β⁻ activity acquired by the solution. The results of the exchange between a chemical γ MnO₂ and a divalent M²⁺ ion (M=Mn, Co, Cu or Zn) or a trivalent M³⁺ ion (M=Ga, Fe, In, Rh or Al) indicate a fast initial process followed by a diffusion—controlled exchange. It is assumed that M²⁺ ions exchange with Mn²⁺ ions and M³⁺ ions exchange with Mn³⁺ ions in MnO₂. The process depends on the radii of the host and substituent ions and on consideration of crystal field stabilisation energies. It seems that the γ MnO₂ studied contains more Mn³⁺ than Mn²⁺ ions. The possibility of the exchange between Mn ions and cations of a different charge cannot be ruled out. The exchange between Co²⁺ ions and MnO₂ was enhanced in presence of pyrophosphate, which stabilises Mn(III) as a complex. The fraction of Mn in different samples of MnO₂ exchanged with a given cation depends on the type and not on the surface area of the sample.     

A review on thiocyanate methods for the estimation of molybdenum by molecular absorption spectroscopy

A review is presented on thiocyanate methods for the estimation of molybdenum in a wide variety of samples. They include conventional thiocyanate methods in which molybdenum forms an orange red complex with the thiocyanate ions and improved thiocyanate methods where the sensitivity is increased through the formation of ternary ion association complex.     

Aquation of α-cis-chloroaquoethylenediamine-N,N'-diacetatocobalt(III) in aqueous and in mixed solvents: A mechanistic study

Summary The displacement of chloride ligands from -cis-chloro-aquoethylenediamine-N,N-diacetatocobalt(III) in nonacidic aqueous solutions was followed conductimetrically at 30–45° and the products of aquation were characterised by conductance, spectral and ion-exchange techniques. The rate constants for aquation in aqueous media and in 1 : 4 v : v mixed solvents at 25° are: 4.0 × 10^–5 s^–1 in H₂O, 2.71 × 10^–5 s^–1 in MeOH : H₂O, 2.74 × 10^–5 s^–1 in EtOH: H₂,O and 2.58 × 10^–5 s^–1 n in Me₂CO : H₂O. The corresponding H* and S* values have also been evaluated. Solvent polarity has a marked influence on the rate of chloride ion release. The aquation rate constants and the activation parameters have been correlated with solvent parameters,e.g. D, Y-values, Dimroth's E_T and Kosower's Z-values and, based on these correlations, a dissociative interchange (I_d) mechanism is proposed rather than dissociative as observed for some other cobalt(III) complexes.Senior author.